FAMILY OF SHAPE PRESERVING FRACTAL-LIKE BÉZIER CURVES.
- Resource Type
- Article
- Authors
- REDDY, K. M.; SARAVANA KUMAR, G.; CHAND, A. K. B.
- Source
- Fractals. Sep2020, Vol. 28 Issue 6, pN.PAG-N.PAG. 18p.
- Subject
- *SUBDIVISION surfaces (Geometry)
*CUBIC curves
*CURVES
*GENERATING functions
*CURVATURE
*CANNING & preserving
- Language
- ISSN
- 0218-348X
Subdivision schemes generate self-similar curves and surfaces for which it has a familiar connection between fractal curves and surfaces generated by iterated function systems (IFS). Overveld [Comput.-Aided Des. 22(9) (1990) 591–597] proved that the subdivision matrices can be perturbated in such a way that it is possible to get fractal-like curves that are perturbated Bézier cubic curves. In this work, we extend the Overveld scheme to n th degree curves, and deduce the condition for curvature continuity and convex hull property. We find the conditions for positive preserving fractal-like Bézier curves in the proposed subdivision matrices. The resulting 2D/3D curves from these binary subdivision matrices resemble with fractal images. Finally, the dependence of the shape of these fractal-like curves on the elements of subdivision matrices is demonstrated with suitably chosen examples. [ABSTRACT FROM AUTHOR]